Physics Letters B 685 (2010) 239–246

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Physics Letters B

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Measurement of the energy spectrum of cosmic rays above 1018 eVusing the Pierre Auger Observatory

Pierre Auger Collaboration a

J. Abraham h, P. Abreu bl, M. Aglietta ay, E.J. Ahn ca, D. Allard aa, J. Allen cd, J. Alvarez-Muñiz bs,M. Ambrosio ar, L. Anchordoqui co, S. Andringa bl, T. Anticic v, A. Anzalone ax, C. Aramo ar,E. Arganda bp, K. Arisaka ci, F. Arqueros bp, H. Asorey b, P. Assis bl, J. Aublin ac, M. Ave ag,cj, G. Avila j,T. Bäcker am, D. Badagnani f, M. Balzer ah, K.B. Barber k, A.F. Barbosa l, S.L.C. Barroso r, B. Baughman cf,P. Bauleo by, J.J. Beatty cf, B.R. Becker cm, K.H. Becker af, A. Bellétoile ad, J.A. Bellido k, S. BenZvi cn,C. Berat ad, T. Bergmann ah, X. Bertou b, P.L. Biermann aj, P. Billoir ac, O. Blanch-Bigas ac, F. Blanco bp,M. Blanco bq, C. Bleve aq, H. Blümer ai,ag, M. Bohácová cj,x, D. Boncioli as, C. Bonifazi u,ac, R. Bonino ay,N. Borodai bj, J. Brack by, P. Brogueira bl, W.C. Brown bz, R. Bruijn bu, P. Buchholz am, A. Bueno br,R.E. Burton bw, N.G. Busca aa, K.S. Caballero-Mora ai, L. Caramete aj, R. Caruso at, A. Castellina ay,O. Catalano ax, G. Cataldi aq, L. Cazon bl,cj, R. Cester au, J. Chauvin ad, A. Chiavassa ay, J.A. Chinellato p,A. Chou ca,cd, J. Chudoba x, R.W. Clay k, E. Colombo c, M.R. Coluccia aq, R. Conceição bl, F. Contreras i,H. Cook bu, M.J. Cooper k, J. Coppens bf,bh, A. Cordier ab, U. Cotti bd, S. Coutu cg, C.E. Covault bw,A. Creusot bn, A. Criss cg, J. Cronin cj, A. Curutiu aj, S. Dagoret-Campagne ab, R. Dallier ae, K. Daumiller ag,B.R. Dawson k, R.M. de Almeida p, M. De Domenico at, C. De Donato be,ap, S.J. de Jong bf, G. De La Vega h,W.J.M. de Mello Junior p, J.R.T. de Mello Neto u, I. De Mitri aq, V. de Souza n, K.D. de Vries bg,G. Decerprit aa, L. del Peral bq, O. Deligny z, A. Della Selva ar, C. Delle Fratte as, H. Dembinski ak,C. Di Giulio as, J.C. Diaz cc, M.L. Díaz Castro m, P.N. Diep cp, C. Dobrigkeit p, J.C. D’Olivo be, P.N. Dong cp,z,A. Dorofeev by, J.C. dos Anjos l, M.T. Dova f, D. D’Urso ar, I. Dutan aj, M.A. DuVernois ck, J. Ebr x, R. Engel ag,M. Erdmann ak, C.O. Escobar p, A. Etchegoyen c, P. Facal San Luis cj,bs, H. Falcke bf,bi, G. Farrar cd,A.C. Fauth p, N. Fazzini ca, A. Ferrero c, B. Fick cc, A. Filevich c, A. Filipcic bm,bn, I. Fleck am, S. Fliescher ak,C.E. Fracchiolla by, E.D. Fraenkel bg, U. Fröhlich am, W. Fulgione ay, R.F. Gamarra c, S. Gambetta an,B. García h, D. García Gámez br, D. Garcia-Pinto bp, X. Garrido ag,ab, G. Gelmini ci, H. Gemmeke ah,P.L. Ghia z,ay, U. Giaccari aq, M. Giller bk, H. Glass ca, L.M. Goggin co, M.S. Gold cm, G. Golup b,F. Gomez Albarracin f, M. Gómez Berisso b, P. Gonçalves bl, D. Gonzalez ai, J.G. Gonzalez br,cb, D. Góra ai,bj,A. Gorgi ay, P. Gouffon o, S.R. Gozzini bu, E. Grashorn cf, S. Grebe bf, M. Grigat ak, A.F. Grillo az,Y. Guardincerri e, F. Guarino ar, G.P. Guedes q, J.D. Hague cm, V. Halenka y, P. Hansen f, D. Harari b,S. Harmsma bg,bh, J.L. Harton by, A. Haungs ag, T. Hebbeker ak, D. Heck ag, A.E. Herve k, C. Hojvat ca,V.C. Holmes k, P. Homola bj, J.R. Hörandel bf, A. Horneffer bf, M. Hrabovský y,x, T. Huege ag, M. Hussain bn,M. Iarlori ao, A. Insolia at, F. Ionita cj, A. Italiano at, S. Jiraskova bf, K. Kadija v, M. Kaducak ca,K.H. Kampert af, T. Karova x, P. Kasper ca, B. Kégl ab, B. Keilhauer ag, A. Keivani cb, J. Kelley bf, E. Kemp p,R.M. Kieckhafer cc, H.O. Klages ag, M. Kleifges ah, J. Kleinfeller ag, R. Knapik by, J. Knapp bu, D.-H. Koang ad,A. Krieger c, O. Krömer ah, D. Kruppke-Hansen af, F. Kuehn ca, D. Kuempel af, K. Kulbartz al, N. Kunka ah,A. Kusenko ci, G. La Rosa ax, C. Lachaud aa, B.L. Lago u, P. Lautridou ae, M.S.A.B. Leão t, D. Lebrun ad,P. Lebrun ca, J. Lee ci, M.A. Leigui de Oliveira t, A. Lemiere z, A. Letessier-Selvon ac, I. Lhenry-Yvon z,R. López bb, A. Lopez Agüera bs, K. Louedec ab, J. Lozano Bahilo br, A. Lucero ay, M. Ludwig ai, H. Lyberis z,M.C. Maccarone ax, C. Macolino ac,ao, S. Maldera ay, D. Mandat x, P. Mantsch ca, A.G. Mariazzi f,

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240 Pierre Auger Collaboration / Physics Letters B 685 (2010) 239–246

V. Marin ae, I.C. Maris ac,ai, H.R. Marquez Falcon bd, G. Marsella av, D. Martello aq, O. Martínez Bravo bb,H.J. Mathes ag, J. Matthews cb,ch, J.A.J. Matthews cm, G. Matthiae as, D. Maurizio au, P.O. Mazur ca,M. McEwen bq, G. Medina-Tanco be, M. Melissas ai, D. Melo au, E. Menichetti au, A. Menshikov ah,C. Meurer ak, S. Micanovic v, M.I. Micheletti c, W. Miller cm, L. Miramonti ap, S. Mollerach b,M. Monasor cj,bp, D. Monnier Ragaigne ab, F. Montanet ad, B. Morales be, C. Morello ay, E. Moreno bb,J.C. Moreno f, C. Morris cf, M. Mostafá by, S. Mueller ag, M.A. Muller p, R. Mussa au, G. Navarra ay,1,J.L. Navarro br, S. Navas br, P. Necesal x, L. Nellen be, P.T. Nhung cp, N. Nierstenhoefer af, D. Nitz cc,D. Nosek w, L. Nožka x, M. Nyklicek x, J. Oehlschläger ag, A. Olinto cj, P. Oliva af, V.M. Olmos-Gilbaja bs,M. Ortiz bp, N. Pacheco bq, D. Pakk Selmi-Dei p, M. Palatka x, J. Pallotta d, N. Palmieri ai, G. Parente bs,E. Parizot aa, S. Parlati az, A. Parra bs, J. Parrisius ai, R.D. Parsons bu, S. Pastor bo, T. Paul ce, V. Pavlidou cj,2,K. Payet ad, M. Pech x, J. Pekala bj, R. Pelayo bs, I.M. Pepe s, L. Perrone av, R. Pesce an, E. Petermann cl,S. Petrera ao,aw, P. Petrinca as, A. Petrolini an, Y. Petrov by, J. Petrovic bh, C. Pfendner cn, R. Piegaia e,T. Pierog ag, M. Pimenta bl, V. Pirronello at, M. Platino c, V.H. Ponce b, M. Pontz am, P. Privitera cj,M. Prouza x, E.J. Quel d, J. Rautenberg af, O. Ravel ae, D. Ravignani c, A. Redondo bq, B. Revenu ae,F.A.S. Rezende l, J. Ridky x, S. Riggi at, M. Risse am,af, P. Ristori d, C. Rivière ad, V. Rizi ao, C. Robledo bb,G. Rodriguez bs,as, J. Rodriguez Martino i,at, J. Rodriguez Rojo i, I. Rodriguez-Cabo bs,M.D. Rodríguez-Frías bq, G. Ros bq, J. Rosado bp, T. Rossler y, M. Roth ag, B. Rouillé-d’Orfeuil cj,aa,E. Roulet b, A.C. Rovero g, F. Salamida ag,ao, H. Salazar bb,3, G. Salina as, F. Sánchez c,be, M. Santander i,C.E. Santo bl, E. Santos bl, E.M. Santos u, F. Sarazin bx, S. Sarkar bt, R. Sato i, N. Scharf ak, V. Scherini af,H. Schieler ag, P. Schiffer ak, A. Schmidt ah, F. Schmidt cj, T. Schmidt ai, O. Scholten bg, H. Schoorlemmer bf,J. Schovancova x, P. Schovánek x, F. Schroeder ag, S. Schulte ak, F. Schüssler ag,∗, D. Schuster bx,S.J. Sciutto f, M. Scuderi at, A. Segreto ax, D. Semikoz aa, M. Settimo aq, R.C. Shellard l,m, I. Sidelnik c,B.B. Siffert u, G. Sigl al, A. Smiałkowski bk, R. Šmída ag,x, G.R. Snow cl, P. Sommers cg, J. Sorokin k,H. Spinka bv,ca, R. Squartini i, J. Stasielak bj, M. Stephan ak, E. Strazzeri ax,ab, A. Stutz ad, F. Suarez c,T. Suomijärvi z, A.D. Supanitsky be, T. Šuša v, M.S. Sutherland cf, J. Swain ce, Z. Szadkowski af,bk,A. Tamashiro g, A. Tamburro ai, A. Tapia c, T. Tarutina f, O. Tascau af, R. Tcaciuc am, D. Tcherniakhovski ah,D. Tegolo at,ba, N.T. Thao cp, D. Thomas by, J. Tiffenberg e, C. Timmermans bh,bf, W. Tkaczyk bk,C.J. Todero Peixoto t, B. Tomé bl, A. Tonachini au, P. Travnicek x, D.B. Tridapalli o, G. Tristram aa, E. Trovato at,M. Tueros f, R. Ulrich cg,ag, M. Unger ag, M. Urban ab, J.F. Valdés Galicia be, I. Valiño ag, L. Valore ar,A.M. van den Berg bg, J.R. Vázquez bp, R.A. Vázquez bs, D. Veberic bn,bm, T. Venters cj, V. Verzi as,M. Videla h, L. Villaseñor bd, S. Vorobiov bn, L. Voyvodic ca,1, H. Wahlberg f, P. Wahrlich k, O. Wainberg c,D. Warner by, A.A. Watson bu, S. Westerhoff cn, B.J. Whelan k, G. Wieczorek bk, L. Wiencke bx,B. Wilczynska bj, H. Wilczynski bj, C. Williams cj, T. Winchen ak, M.G. Winnick k, B. Wundheiler c,T. Yamamoto cj,4, P. Younk by, G. Yuan cb, A. Yushkov ar, E. Zas bs, D. Zavrtanik bn,bm, M. Zavrtanik bm,bn,I. Zaw cd, A. Zepeda bc, M. Ziolkowski am

a Observatorio Pierre Auger, Av. San Martin Norte 304, 5613 Malargüe, Argentinab Centro Atómico Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de Bariloche, Argentinac Centro Atómico Constituyentes (Comisión Nacional de Energía Atómica/CONICET/UTN-FRBA), Buenos Aires, Argentinad Centro de Investigaciones en Láseres y Aplicaciones, CITEFA and CONICET, Argentinae Departamento de Física, FCEyN, Universidad de Buenos Aires y CONICET, Argentinaf IFLP, Universidad Nacional de La Plata and CONICET, La Plata, Argentinag Instituto de Astronomía y Física del Espacio (CONICET), Buenos Aires, Argentinah National Technological University, Faculty Mendoza (CONICET/CNEA), Mendoza, Argentinai Pierre Auger Southern Observatory, Malargüe, Argentinaj Pierre Auger Southern Observatory and Comisión Nacional de Energía Atómica, Malargüe, Argentinak University of Adelaide, Adelaide, S.A., Australial Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, RJ, Brazilm Pontifícia Universidade Católica, Rio de Janeiro, RJ, Braziln Universidade de São Paulo, Instituto de Física, São Carlos, SP, Brazilo Universidade de São Paulo, Instituto de Física, São Paulo, SP, Brazilp Universidade Estadual de Campinas, IFGW, Campinas, SP, Brazilq Universidade Estadual de Feira de Santana, Brazilr Universidade Estadual do Sudoeste da Bahia, Vitoria da Conquista, BA, Brazils Universidade Federal da Bahia, Salvador, BA, Brazilt Universidade Federal do ABC, Santo André, SP, Brazilu Universidade Federal do Rio de Janeiro, Instituto de Física, Rio de Janeiro, RJ, Brazilv Rudjer Boškovic Institute, 10000 Zagreb, Croatiaw Charles University, Faculty of Mathematics and Physics, Institute of Particle and Nuclear Physics, Prague, Czech Republicx Institute of Physics of the Academy of Sciences of the Czech Republic, Prague, Czech Republicy Palacký University, Olomouc, Czech Republic

Pierre Auger Collaboration / Physics Letters B 685 (2010) 239–246 241

z Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris 11, CNRS-IN2P3, Orsay, Franceaa Laboratoire AstroParticule et Cosmologie (APC), Université Paris 7, CNRS-IN2P3, Paris, Franceab Laboratoire de l’Accélérateur Linéaire (LAL), Université Paris 11, CNRS-IN2P3, Orsay, Franceac Laboratoire de Physique Nucléaire et de Hautes Energies (LPNHE), Universités Paris 6 et Paris 7, CNRS-IN2P3, Paris, Francead Laboratoire de Physique Subatomique et de Cosmologie (LPSC), Université Joseph Fourier, INPG, CNRS-IN2P3, Grenoble, Franceae SUBATECH, CNRS-IN2P3, Nantes, Franceaf Bergische Universität Wuppertal, Wuppertal, Germanyag Karlsruhe Institute of Technology – Campus North – Institut für Kernphysik, Karlsruhe, Germanyah Karlsruhe Institute of Technology – Campus North – Institut für Prozessdatenverarbeitung und Elektronik, Karlsruhe, Germanyai Karlsruhe Institute of Technology – Campus South – Institut für Experimentelle Kernphysik (IEKP), Karlsruhe, Germanyaj Max-Planck-Institut für Radioastronomie, Bonn, Germanyak RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germanyal Universität Hamburg, Hamburg, Germanyam Universität Siegen, Siegen, Germanyan Dipartimento di Fisica dell’Università and INFN, Genova, Italyao Università dell’Aquila and INFN, L’Aquila, Italyap Università di Milano and Sezione INFN, Milan, Italyaq Dipartimento di Fisica dell’Università del Salento and Sezione INFN, Lecce, Italyar Università di Napoli “Federico II” and Sezione INFN, Napoli, Italyas Università di Roma II “Tor Vergata” and Sezione INFN, Roma, Italyat Università di Catania and Sezione INFN, Catania, Italyau Università di Torino and Sezione INFN, Torino, Italyav Dipartimento di Ingegneria dell’Innovazione dell’Università del Salento and Sezione INFN, Lecce, Italyaw Gran Sasso Center for Astroparticle Physics, Italyax Istituto di Astrofisica Spaziale e Fisica Cosmica di Palermo (INAF), Palermo, Italyay Istituto di Fisica dello Spazio Interplanetario (INAF), Università di Torino and Sezione INFN, Torino, Italyaz INFN, Laboratori Nazionali del Gran Sasso, Assergi (L’Aquila), Italyba Università di Palermo and Sezione INFN, Catania, Italybb Benemérita Universidad Autónoma de Puebla, Puebla, Mexicobc Centro de Investigación y de Estudios Avanzados del IPN (CINVESTAV), México, D.F., Mexicobd Universidad Michoacana de San Nicolas de Hidalgo, Morelia, Michoacan, Mexicobe Universidad Nacional Autonoma de Mexico, Mexico, D.F., Mexicobf IMAPP, Radboud University, Nijmegen, Netherlandsbg Kernfysisch Versneller Instituut, University of Groningen, Groningen, Netherlandsbh NIKHEF, Amsterdam, Netherlandsbi ASTRON, Dwingeloo, Netherlandsbj Institute of Nuclear Physics PAN, Krakow, Polandbk University of Łódz, Łódz, Polandbl LIP and Instituto Superior Técnico, Lisboa, Portugalbm J. Stefan Institute, Ljubljana, Sloveniabn Laboratory for Astroparticle Physics, University of Nova Gorica, Sloveniabo Instituto de Física Corpuscular, CSIC-Universitat de València, Valencia, Spainbp Universidad Complutense de Madrid, Madrid, Spainbq Universidad de Alcalá, Alcalá de Henares (Madrid), Spainbr Universidad de Granada & C.A.F.P.E., Granada, Spainbs Universidad de Santiago de Compostela, Spainbt Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, United Kingdombu School of Physics and Astronomy, University of Leeds, United Kingdombv Argonne National Laboratory, Argonne, IL, USAbw Case Western Reserve University, Cleveland, OH, USAbx Colorado School of Mines, Golden, CO, USAby Colorado State University, Fort Collins, CO, USAbz Colorado State University, Pueblo, CO, USAca Fermilab, Batavia, IL, USAcb Louisiana State University, Baton Rouge, LA, USAcc Michigan Technological University, Houghton, MI, USAcd New York University, New York, NY, USAce Northeastern University, Boston, MA, USAcf Ohio State University, Columbus, OH, USAcg Pennsylvania State University, University Park, PA, USAch Southern University, Baton Rouge, LA, USAci University of California, Los Angeles, CA, USAcj University of Chicago, Enrico Fermi Institute, Chicago, IL, USAck University of Hawaii, Honolulu, HI, USAcl University of Nebraska, Lincoln, NE, USAcm University of New Mexico, Albuquerque, NM, USAcn University of Wisconsin, Madison, WI, USAco University of Wisconsin, Milwaukee, WI, USAcp Institute for Nuclear Science and Technology (INST), Hanoi, Viet Nam

a r t i c l e i n f o a b s t r a c t

Article history:Received 26 November 2009Accepted 4 February 2010Available online 10 February 2010Editor: S. Dodelson

We report a measurement of the flux of cosmic rays with unprecedented precision and statistics usingthe Pierre Auger Observatory. Based on fluorescence observations in coincidence with at least one surfacedetector we derive a spectrum for energies above 1018 eV. We also update the previously publishedenergy spectrum obtained with the surface detector array. The two spectra are combined addressing thesystematic uncertainties and, in particular, the influence of the energy resolution on the spectral shape.

242 Pierre Auger Collaboration / Physics Letters B 685 (2010) 239–246

Keywords:Pierre Auger ObservatoryCosmic raysEnergy spectrum

The spectrum can be described by a broken power law E−γ with index γ = 3.3 below the ankle whichis measured at log10(Eankle/eV) = 18.6. Above the ankle the spectrum is described by a power law withindex 2.6 followed by a flux suppression, above about log10(E/eV) = 19.5, detected with high statisticalsignificance.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

The flux of ultra-high energy cosmic rays exhibits two im-portant features. At energies above 4 × 1019 eV a suppression ofthe flux with respect to a power law extrapolation is found [1,2],which is compatible with the predicted Greisen–Zatsepin–Kuz’min(GZK) effect [3,4], but could also be related to the maximum en-ergy that can be reached at the sources. A break in the power law,called the ankle, is observed at an energy of about 3 × 1018 eV[5–8]. This break in the energy spectrum has traditionally beenattributed to the transition from the galactic component of the cos-mic ray flux to a flux dominated by extragalactic sources [9,10]. Inrecent years it became clear that a similar feature in the cosmic rayspectrum could also result from the propagation of protons fromextragalactic sources, placing the transition from galactic to extra-galactic cosmic rays at a much lower energy [11,12]. In this modelthe ankle is produced by the modification of the source spectrumof primary protons. This is caused by e± pair production of protonswith the photons of the cosmic microwave background, leading toa well-defined prediction of the shape of the flux in the ankle re-gion.

Accurate measurement of the cosmic ray flux in the ankle re-gion is expected to help determine the energy range of the tran-sition between galactic and extragalactic cosmic rays and to con-strain model scenarios.

Two complementary techniques are used at the Pierre AugerObservatory to detect extensive air showers initiated by ultra-highenergy cosmic rays (UHECR): a surface detector array (SD) and afluorescence detector (FD). The SD of the southern observatory inArgentina consists of an array of 1600 water Cherenkov detec-tors covering an area of about 3000 km2 on a triangular grid with1.5 km spacing. Electrons, photons and muons in air showers aresampled at ground level with a on-time of almost 100%. In addi-tion the atmosphere above the surface detector is observed duringclear, dark nights by 24 optical telescopes grouped in 4 buildings.These detectors are used to observe the longitudinal developmentof extensive air showers by detecting the fluorescence light emit-ted by excited nitrogen molecules and the Cherenkov light inducedby the shower particles. Details of the design and status of the Ob-servatory are given elsewhere [13–15].

The energy spectrum of ultra-high energy cosmic rays at ener-gies greater than 2.5 × 1018 eV has been derived using data fromthe surface detector array of the Pierre Auger Observatory [2]. Thismeasurement provided evidence for the suppression of the fluxabove 4 × 1019 eV and is updated here. In this work we extend theprevious measurements to lower energies by analysing air show-ers measured with the fluorescence detector that also triggered atleast one of the stations of the surface detector array. Despite thelimited event statistics due to the fluorescence detector on-time ofabout 13%, the lower energy threshold and the good energy resolu-

* Corresponding author.E-mail address: fabian.schuessler@ik.fzk.de (F. Schüssler).

1 Deceased.2 At Caltech, Pasadena, USA.3 On leave of absence at the Instituto Nacional de Astrofisica, Optica y Electronica.4 At Konan University, Kobe, Japan.

tion of these hybrid events allow us to measure the flux of cosmicrays in the region of the ankle.

The energy spectrum of hybrid events is determined from datataken between November 2005 and May 2008, during which theAuger Observatory was still under construction. Using selection cri-teria that are set out below, the exposure accumulated during thisperiod was computed and the flux of cosmic rays above 1018 eVdetermined. The spectrum obtained with the surface detector ar-ray, updated using data until the end of December 2008, is com-bined with the hybrid one to obtain a spectrum measurement overa wide energy range with the highest statistics available.

2. Hybrid energy spectrum

The hybrid approach to shower observation is based on theshower detection with the FD in coincidence with at least oneSD station. The latter condition, though insufficient to establish anindependent SD trigger [2,16], enables the shower geometry andconsequently the energy of the primary particle to be determinedaccurately. The reconstruction accuracy of hybrid events is muchbetter than what can be achieved using SD or FD data indepen-dently [17]. For example, the energy resolution of these hybridmeasurements is better than 6% above 1018 eV compared withabout 15% for the surface detector data.

Event reconstruction proceeds in two steps. First the showergeometry is found by combining information from the shower im-age and timing measured with the FD with the trigger time ofthe surface detector station that has the largest signal [18]. Inthe second step the profile of energy deposition of the showeris reconstructed [19] and shower parameters such as depth ofshower maximum and primary particle energy are calculated to-gether with their uncertainties.

2.1. Event selection and reconstruction

To ensure good energy reconstruction only events that satisfythe following quality criteria are accepted:

• Showers must have a reconstructed zenith angle smaller than60◦ .

• In the plane perpendicular to the shower axis, the recon-structed shower core must be within 1500 m of the stationused for the geometrical reconstruction.

• The contribution of Cherenkov light to the overall signal of theFD must be less than 50%.

• The Gaisser–Hillas fit [19,20] of the reconstructed longitudinalprofile must be successful with χ2/ndof < 2.5.

• The maximum of the shower development, Xmax, must be ob-served in the field of view of the telescopes.

• The uncertainty in the reconstructed energy, which includeslight flux and geometrical uncertainties, must be σ(E)/E <

20%.• Only periods during which no clouds were detected above the

Observatory are used.

To avoid a possible bias in event selection due to the differ-ences between shower profiles initiated by primaries of different

Pierre Auger Collaboration / Physics Letters B 685 (2010) 239–246 243

mass, only showers with geometries that would allow the obser-vation of all primaries in the range from proton to iron are retainedin the data sample. The corresponding fiducial volume in shower-telescope distance and zenith angle range is defined as a functionof the reconstructed energy and has been verified with data [21].About 1700 events fulfill the selection criteria for quality and forfiducial volume.

A detailed simulation of the detector response has shown thatevery FD trigger above E = 1018 eV passing all the described selec-tion criteria is accompanied by a SD trigger of at least one station,independent of the mass and direction of the incoming primaryparticle [22].

2.2. Exposure calculation

During the time period discussed here the southern Auger Ob-servatory was in its construction phase with the number of avail-able SD stations increasing from around 630 to a nearly fully com-pleted instrument with 1600 detectors. Over the same period theFD was enlarged from 12 to 24 telescopes. In addition to theselarge scale changes, smaller but important changes occur on muchshorter timescales due, for example, to hardware failures. The data-taking of the fluorescence detector is furthermore influenced byweather effects such as storms or rainfall. These and other factorsthat affect the efficiency of the data-taking must be taken into ac-count in the determination of the aperture.

The total exposure is the integral over the instantaneous aper-ture and can be written as

E (E) =∫

T

∫

Ω

∫

Sgen

ε(E, t, θ,φ, x, y) cos θ dS dΩ dt, (1)

where dΩ = sin θ dθ dφ and Ω are respectively the differential andtotal solid angles, θ and φ are the zenith and azimuth angles anddS = dx × dy is the horizontal surface element. The final selec-tion efficiency ε includes the efficiencies of the various steps ofthe analysis, namely the trigger, reconstruction and selection ef-ficiencies and also the evolution of the detector during the timeperiod T . It has been derived from Monte Carlo simulations thatscan an area Sgen large enough to enclose the full detector array.

The changing configuration of the SD array is taken into accountfor the determination of the hybrid on-time. In addition, withintime intervals of 10 min, the status of all detector components ofthe Pierre Auger Observatory down to the level of single PMTs ofthe fluorescence detector is determined. Moreover all known inef-ficiencies such as DAQ read-out deadtimes are considered.

The longitudinal profile of the deposition of energy simulatedwith the QGSJet-II [23,24] and Sibyll 2.1 [25,26] hadronic interac-tion models and the CONEX [27] air shower simulation programare the basis for an extensive set of Monte Carlo simulations. Theexact data taking conditions are reproduced by means of a detaileddetector simulation within the Auger analysis framework [28]. Allatmospheric measurements, e.g. scattering and absorption lengths,as well as monitoring information such as the noise caused bynight sky background light and PMT trigger thresholds are takeninto account.

The reconstruction of the simulated showers is then performedin exactly the same way as for the data and good agreement be-tween data and Monte Carlo simulations is obtained. As an exam-ple, we show in Fig. 1 the distribution of events observed with thefluorescence detector as a function of the distance of the showercore from the telescopes.

Fig. 2 shows the hybrid exposure of events fulfilling all of thequality and fiducial volume cuts that have been applied, for pro-ton and iron primaries. As can be seen, the cuts adopted lead to

Fig. 1. Distribution of events observed with the fluorescence detector as a functionof the distance of the shower core from the telescopes for data and Monte Carlosimulation.

Fig. 2. The hybrid exposure for different primary particles together with the differ-ence to the mixed composition used for the flux measurement.

only a small dependence of the exposure on the mass composi-tion which can be assumed to be dominated by hadrons [29,30].The systematic uncertainty arising from our lack of knowledge ofthe mass composition is about 8% at 1018 eV and decreases to lessthan 1% above 1019 eV. We assume a mixed composition of 50%proton and 50% iron nuclei for the flux determination and includethe remaining composition dependence in the systematic uncer-tainty. The dependence of the exposure on the assumed model ofhadronic interactions was found to be less than 2% over all theenergy range.

The full MC simulation chain has been cross-checked with airshower observations and the analysis of laser shots that are firedfrom the Central Laser Facility [31] and detected with the fluo-rescence detector. Following this analysis the exposure has beenreduced by 8% to account for lost events and an upper limit tothe remaining systematic uncertainty of 5% was derived [32]. Bycombination with the uncertainty related to mass composition thetotal systematic uncertainty of the hybrid exposure is estimated as10% (6%) at 1018 eV (> 1019 eV).

244 Pierre Auger Collaboration / Physics Letters B 685 (2010) 239–246

2.3. Energy spectrum from hybrid data

The flux of cosmic rays J as a function of energy is given by

J (E) = d4Ninc

dE dA dΩ dt∼= Nsel(E)

E

1

E (E), (2)

where Ninc is the number of cosmic rays with energy E incidenton a surface element dA, within a solid angle dΩ and time dt .Nsel(E) is the number of detected events passing the quality cutsin the energy bin centered around E and having width E . E (E) isthe energy-dependent exposure defined above.

The measured flux as function of energy is shown in Fig. 3.A break in the power law of the derived energy spectrum isclearly visible. The position of this feature, known as the ankle,has been determined by fitting two power laws J = kE−γ witha free break between them in the energy interval from 1018 eVto 1019.5 eV. The upper end of this interval was defined by theflux suppression observed in the spectrum derived using sur-face detector data [2]. The ankle is found at log10(Eankle/eV) =18.65 ± 0.09(stat)+0.10

−0.11(sys) and the two power law indices have

been determined as γ1 = 3.28 ± 0.07(stat)+0.11−0.10(sys) and γ2 =

2.65±0.14(stat)+0.16−0.14(sys) (χ2/ndof = 10.2/11), where the system-

atic uncertainty is due to the residual effect of the unknown masscomposition.

The energy estimation of fluorescence measurements relies onthe knowledge of the fluorescence yield. Here we adopt the sameabsolute calibration [33] and the wavelength and pressure depen-dence [34] as in Ref. [2]. This is currently one of the dominantsources of systematic uncertainty (14%). The fraction of the en-ergy of the primary particle that is carried by muons and neutrinosand does not contribute to the fluorescence signal has been calcu-lated based on air shower simulations and goes from about 14% at1018 eV to about 10% at 1019 eV [35]. The systematic uncertaintydepending on the choice of models and mass composition is about8% [36]. Further systematic uncertainties in the absolute energyscale are related to the absolute detector calibration (9.5%) andits wavelength dependence (3%) [37]. Uncertainties of the lateralwidth of the shower image and other reconstruction uncertaintiesamount to about 10% systematic uncertainty in the energy deter-mination. Atmospheric conditions play a crucial role for air showerobservations with fluorescence detectors. An extensive program ofatmospheric monitoring is conducted at the Pierre Auger Obser-vatory allowing the determination of the relevant parameters andthe associated uncertainties [31,38–40]. The total systematic un-certainty in the energy determination is estimated as 22% [41].Indirect methods of determining the energy scale, which do notinvolve the fluorescence detector calibration, seem to indicate anenergy normalisation that is higher than the one used here by anamount comparable to the uncertainty given above [42].

3. Update of surface detector spectrum

Here we update the published energy spectrum based on sur-face detector data [2] using data until the end of December 2008.The exposure is now 12 790 km2 sr yr. The event selection requiresthat the detector station with the highest signal be surroundedby operational stations and that the reconstructed zenith angle besmaller than 60◦ [16]. More than 35 000 events fulfill these crite-ria.

The energy estimator of the surface detector is corrected forshower attenuation effects using a constant-intensity method. Thecalibration of this energy estimator with fluorescence measure-ments has been updated using the increased data set of high-quality hybrid events [41].

Fig. 3. The energy spectrum of ultra-high energy cosmic rays determined from hy-brid measurements of the Pierre Auger Observatory. The number of events is givenfor each of the energy bins next to the corresponding data point. Only statisticaluncertainties are shown. The upper limits correspond to the 68% CL. A fit with abroken power law is used to determine the position of the ankle.

Fig. 4. Energy spectrum, corrected for energy resolution, derived from surface detec-tor data calibrated with fluorescence measurements. The number of events is givenfor each of the energy bins next to the corresponding data point. Only statisticaluncertainties are shown. The upper limits correspond to 68% CL.

Because of the energy resolution of the surface detector data(about 20% at the lowest energies, improving to about 10% at thehighest energies), bin-to-bin migrations influence the reconstruc-tion of the flux and spectral shape. To correct for these effects,a forward-folding approach is applied. MC simulations are usedto determine the energy resolution of the surface detector and abin-to-bin migration matrix is derived. The matrix is then used tofind a flux parameterisation that matches the measured data afterforward-folding. The ratio of this parameterisation to the foldedflux gives a correction factor that is applied to the data. The cor-rection to the flux is mildly energy dependent and is less than 20%over the full energy range. Details will be discussed in a forthcom-ing publication.

The energy spectrum, after correction for the energy resolution,is shown in Fig. 4 together with the event numbers of the un-

Pierre Auger Collaboration / Physics Letters B 685 (2010) 239–246 245

Fig. 5. The combined energy spectrum is fitted with two functions (see text) andcompared to data from the HiRes instrument [43]. The systematic uncertainty ofthe flux scaled by E3 due to the uncertainty of the energy scale of 22% is indicatedby arrows. A table with the Auger flux values can be found at [44].

derlying raw distribution. Combining the systematic uncertaintiesof the exposure (3%) and of the forward folding assumptions (5%),the systematic uncertainty of the derived flux is 6%.

4. The combined Auger spectrum

The energy spectrum derived from hybrid data is combinedwith the one obtained from surface detector data using a max-imum likelihood method. Since the surface detector energy esti-mator is calibrated with hybrid events, the two spectra have thesame systematic uncertainty in the energy scale. On the otherhand, the normalisation uncertainties are independent. They aretaken as 6% for the SD and 10% (6%) for the hybrid flux at 1018 eV(> 1019 eV). These normalisation uncertainties are used as addi-tional constraints in the combination. This combination procedureis used to derive the scale parameters, k, for the fluxes that areto be applied to the individual spectra. These are kSD = 1.01 andkFD = 0.99 for the surface detector data and hybrid data respec-tively, showing that agreement between the measurements is atthe 1% level.

The combined energy spectrum scaled with E3 is shown inFig. 5 in comparison with the spectrum obtained with stereo mea-surements of the HiRes instrument [43]. An energy shift within thecurrent systematic uncertainties of the energy scale applied to oneor both experiments could account for most of the difference be-tween the spectra. The ankle feature seems to be somewhat moresharply defined in the Auger data. This is possibly due to a sys-tematic energy offset between the experiments. However, for acomplete comparison, care must also be taken to account for en-ergy resolution and possible changes in aperture with energy.

The characteristic features of the combined spectrum are quan-tified in two ways. For the first method, shown as a dotted red linein Fig. 5, we have used three power laws with free breaks betweenthem. A continuation of the power law above the ankle to high-est energies can be rejected with more than 20σ . For the secondcharacterisation we have adopted two power laws in the ankle re-gion and a smoothly changing function at higher energies which isgiven by

J (E; E > Eankle) ∝ E−γ2

1 + exp(log10 E−log10 E1/2 )

, (3)

log10 Wc

Table 1Fitted parameters and their statistical uncertainties characterising the combined en-ergy spectrum.

Parameter Power laws Power laws +smooth function

γ1(E < Eankle) 3.26 ± 0.04 3.26 ± 0.04log10(Eankle/eV) 18.61 ± 0.01 18.60 ± 0.01γ2(E > Eankle) 2.59 ± 0.02 2.55 ± 0.04log10(Ebreak/eV) 19.46 ± 0.03γ3(E > Ebreak) 4.3 ± 0.2log10(E1/2/eV) 19.61 ± 0.03log10(Wc/eV) 0.16 ± 0.03χ2/ndof 38.5/16 29.1/16

where E1/2 is the energy at which the flux has fallen to one half ofthe value of the power-law extrapolation and Wc parametrizes thewidth of the transition region. It is shown as a black solid line inFig. 5. The derived parameters (quoting only statistical uncertain-ties) are given in Table 1.

At high energies the combined spectrum is statistically domi-nated by the surface detector data. The agreement between the in-dex of the power law above the ankle, γ2, measured with the com-bined spectrum (2.59 ± 0.02) and with hybrid data (2.65 ± 0.14),also demonstrates the good agreement between the two measure-ments.

5. Summary

We have measured the cosmic ray flux with the Pierre AugerObservatory by applying two different techniques. The fluxes ob-tained with hybrid events and from the surface detector array arein good agreement in the overlapping energy range. A combinedspectrum has been derived with high statistics covering the energyrange from 1018 eV to above 1020 eV. The dominant systematicuncertainty of the spectrum stems from that of the overall energyscale, which is estimated to be 22%.

The position of the ankle at log10(Eankle/eV) = 18.61 ± 0.01 hasbeen determined by fitting the flux with a broken power law E−γ .An index of γ = 3.26 ± 0.04 is found below the ankle. Above theankle the spectrum follows a power law with index 2.55 ± 0.04.In comparison to the power law extrapolation, the spectrum issuppressed by a factor two at log10(E1/2/eV) = 19.61 ± 0.03. Thesignificance of the suppression is larger than 20σ . The suppres-sion is similar to what is expected from the GZK effect for protonsor nuclei as heavy as iron, but could in part also be related toa change of the shape of the average injection spectrum at thesources.

Acknowledgements

The successful installation and commissioning of the PierreAuger Observatory would not have been possible without thestrong commitment and effort from the technical and administra-tive staff in Malargüe.

We are very grateful to the following agencies and organiza-tions for financial support: Comisión Nacional de Energía Atómica,Fundación Antorchas, Gobierno De La Provincia de Mendoza, Mu-nicipalidad de Malargüe, NDM Holdings and Valle Las Leñas, ingratitude for their continuing cooperation over land access, Ar-gentina; the Australian Research Council; Conselho Nacional deDesenvolvimento Científico e Tecnológico (CNPq), Financiadora deEstudos e Projetos (FINEP), Fundação de Amparo à Pesquisa do Es-tado de Rio de Janeiro (FAPERJ), Fundação de Amparo à Pesquisado Estado de São Paulo (FAPESP), Ministério de Ciência e Tecnolo-gia (MCT), Brazil; AVCR AV0Z10100502 and AV0Z10100522, GAAVKJB300100801 and KJB100100904, MSMT-CR LA08016, LC527,

246 Pierre Auger Collaboration / Physics Letters B 685 (2010) 239–246

1M06002, and MSM0021620859, Czech Republic; Centre de Cal-cul IN2P3/CNRS, Centre National de la Recherche Scientifique(CNRS), Conseil Régional Ile-de-France, Département PhysiqueNucléaire et Corpusculaire (PNC-IN2P3/CNRS), Département Sci-ences de l’Univers (SDU-INSU/CNRS), France; Bundesministeriumfür Bildung und Forschung (BMBF), Deutsche Forschungsgemein-schaft (DFG), Finanzministerium Baden-Württemberg, Helmholtz-Gemeinschaft Deutscher Forschungszentren (HGF), Ministerium fürWissenschaft und Forschung, Nordrhein-Westfalen, Ministeriumfür Wissenschaft, Forschung und Kunst, Baden-Württemberg, Ger-many; Istituto Nazionale di Fisica Nucleare (INFN), Ministero del-l’Istruzione, dell’Università e della Ricerca (MIUR), Italy; ConsejoNacional de Ciencia y Tecnología (CONACYT), Mexico; Ministerievan Onderwijs, Cultuur en Wetenschap, Nederlandse Organisatievoor Wetenschappelijk Onderzoek (NWO), Stichting voor Funda-menteel Onderzoek der Materie (FOM), Netherlands; Ministry ofScience and Higher Education, Grant Nos. 1 P03 D 014 30, N202090 31/0623, and PAP/218/2006, Poland; Fundação para a Ciên-cia e a Tecnologia, Portugal; Ministry for Higher Education, Sci-ence, and Technology, Slovenian Research Agency, Slovenia; Co-munidad de Madrid, Consejería de Educación de la Comunidadde Castilla La Mancha, FEDER funds, Ministerio de Ciencia e In-novación, Xunta de Galicia, Spain; Science and Technology Facil-ities Council, United Kingdom; Department of Energy, ContractNos. DE-AC02-07CH11359, DE-FR02-04ER41300, National ScienceFoundation, Grant No. 0450696, The Grainger Foundation, USA;ALFA-EC/HELEN, European Union 6th Framework Program, GrantNo. MEIF-CT-2005-025057, European Union 7th Framework Pro-gram, Grant No. PIEF-GA-2008-220240, and UNESCO.

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